A sum of money was distributed equally in a class of boys. Had there been 10 boys more, each would have received a rupee less. If there had been 15 boys less, each would have received 3 rupees more. Find the sum of money and the number of boys.

# A sum of money was distributed equally in a class of boys. Had there been 10 boys more, each would have received a rupee less. If there had been 15 boys less, each would have received 3 rupees more. Find the sum of money and the number of boys.

1. A
Rs.300
2. B
Rs.200
3. C
Rs.500
4. D
Rs.700

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### Solution:

Let the number of boys be and the total sum of money be rupees.
Sum of money received by each boy Here, the number of boys becomes .
Sum of money received by each boy The sum of money received by each boy (where the number of boys is ) is Re. 1 less than the sum of money received by each boy (where the number of boys is ).
Therefore, we get the equation  Simplifying by cross multiplication, we get Multiplying by using the distributive law of multiplication, we get Subtracting from both sides, we get Rewriting the equation, we get Sum of money received by each boy The sum of money received by each boy (where the number of boys is ) is Re. 1 less than the sum of money received by each boy (where the number of boys is ).
Therefore, we get the equation  Simplifying by cross multiplication, we get Multiplying by using the distributive law of multiplication, we get Subtracting from both sides, we get Dividing both sides by 3 and rewriting the equation, we get Subtracting equation from equation , we get Adding and subtracting the like terms, we get Dividing both sides by 5, we get  Substituting in the equation ,we get    Subtracting from both sides, we get Thus, the number of boys is 40.
Substituting in the equation , we get  The total sum of money is Rs. 200.
So, option 2 is correct.

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